基於梯度優化演算法之抗反射薄膜與高通光學薄膜濾波器之研究

Designs and Implementation of Anti-Reflection Coatings and High-Pass Optical Thin-Film Filters with Gradient Based Optimization Algorithm

蔡俐瑩(Li-Ying Tsai)

指導教授 ： 吳忠幟

國立臺灣大學/電機資訊學院/光電工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101880

摘要

光學薄膜現今已被廣泛應用，從精密的光學儀器至日常生活中的太陽眼鏡皆可見其蹤跡。隨著鍍膜技術的提升，多層膜常用於製作濾波器、抗反射膜等產品，但如何有效的設計可用或需要的多層膜結構依舊是一個困難的挑戰。傳統上而言，可以利用一些已知的結構，如分布式布拉格反射器(distributed Bragg reflector, DBR)或四分之波長之抗反射膜層，然而此種設計只適用於單波長，而無法達成更複雜的應用，有鑑於此本論文將利用梯度法之最佳化演算法來自動化設計光學薄膜之膜層厚度。
在本論文研究的第一部分，我們透過轉移矩陣來計算多層膜結構的穿透係數及反射係數，並定義出合適的目標函數，最後在梯度下降的基礎下引入正向傳播矩陣及反向傳播矩陣以加快梯度計算時間，僅需計算2次轉移矩陣，相較於傳統利用兩點式計算梯度的方法能夠大幅縮短運算時間。
在本論文的第二部分，我們討論如何挑選合適的優化參數，設計出最簡化的薄膜光學結構，並利用RF濺鍍及熱蒸鍍的方式成功做出僅需6-8對高低折射率的高通濾波器，在通帶達到平均穿透度95 % 以上，同時在阻帶達到穿透度接近0 %。此外，在本論文中也利用演算法的方法設計抗反射膜，可以使玻璃基板達到接近透明的程度，在玻璃基板的雙面僅需鍍上2-3對抗反射光學膜，減少介面折射率差所造成的反射，可達到99 % 的高穿透度。最後同時結合高通濾波光學薄膜及抗反射光學薄膜，實做出在通帶可達到穿透度99 %、阻帶低於1 % 之光學元件。

關鍵字

薄膜光學 ； 傳播矩陣 ； 梯度優化 ； 抗反射膜 ； 分布式布拉格反射器 ； 射頻濺鍍沉積

並列摘要

Optical thin films have been widely used in many applications, from optical precision instruments to sun glasses in daily lives. With the advancement of coating technologies, optical multi-layers are often used in optical filters and anti-reflection coatings. However, how to design the desired multi-layer structures effectively is still a challenge. Traditionally, distributed Bragg reflectors or quarter-wavelength anti-reflection coatings can be used, but such designs are only suitable for the single wavelength, not able to achieve more complex applications or characteristics. Therefore, in this thesis, we use the optimization algorithm based on the gradient descent method to design the functional optical thin-film structures.
In the first part of the thesis, we used the transfer matrix to calculate transmittance coefficient and reflection coefficient of the multilayer structure. Next, with defining the proper objective function, we proposed the combination of the forward propagation matrix and backward propagation matrix based on the gradient optimization method to accelerate gradient calculation. It only needs to calculate the transfer matrices twice, which can greatly reduce the calculation time compared with numerical two-point method.
In the second part of the thesis, we discuss how to choose suitable optimization parameters, and design the simplest possible functional optical thin-film structure. We successfully realized high-pass optical filters with only 6-8 high-/low- index pairs of thin films and using the RF sputtering and thermal evaporation deposition, achieving the high transmittance in the pass band (~ 95 %) and nearly 0 % transmittance in the block band. Furthermore, we used the algorithm to design the anti-reflection coating, achieving nearly 99 % transparency for glass substrates, with only 2-3 pairs of multilayers deposited on both sides of glass substrates to reduced the reflection caused by the difference in refractive indexes. Finally, by combining the high pass filter and the anti-reflection coating, the optical components with high transmittance of 99 % in the pass band and transmittance lower than 1 % in the block band.

並列關鍵字

thin-film optics ； transfer matrix ； gradient optimization ； anti-reflection coating ； distributed Bragg reflector ； RF sputtering

參考文獻

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